Abstract
In this paper, the following problem is considered: for a given nondecreasing finite sequence of positive integers, determine if there exists an affine control system whose growth vector coincides with this sequence. The answer is “yes” if and only if the Taylor series of a certain function constructed via elements of the sequence has nonnegative coefficients. It turns out that this problem is closely connected with properties of “core Lie subalgebras” of affine control systems which are responsible for a homogeneous approximation. We give a representation of core Lie subalgebras as free Lie algebras and describe sets of all possible core Lie subalgebras for systems with a fixed growth vector.
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Ignatovich, S.Y. Realizable growth vectors of affine control systems. J Dyn Control Syst 15, 557–585 (2009). https://doi.org/10.1007/s10883-009-9075-y
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DOI: https://doi.org/10.1007/s10883-009-9075-y